[Smt-talk] Classical Form and Recursion

Richard Hermann harhar at unm.edu
Sun Mar 22 10:05:25 PDT 2009

Dear all,

	I find this thread less interesting than it might be because the  
term "recursion" has many different meanings attached to it in  
different fields. My first exposure was in computer programming, and  
descriptions of "recursion" in Schenkerian thought made little sense  
to me at first because of my initial exposure to the term. In such  
circumstances, it is easy to pull out a definition that will tank  
someone else's position. I believe philosophers call this  
"equivocation of terms."
	Thomas, how was this problem addressed at the conference? It must  
have been very stimulating.


Richard Hermann, Prof. of Music
Univ. of New Mexico

On Mar 22, 2009, at 5:19 AM, Dave Headlam wrote:

> Dear Thomas:   I would suggest a few things, of couRsE starting  
> with not a CURSery romp through the Inimitable VolumE “Godel Escher  
> Bach” by Hofstadter:
> In an article I wrote for Spectrum 7 I noted the affinity between  
> the opening Rhythm of Beethoven’s opus 59, no. 1 / II and the  
> exposition, both of which (I now think) are sentence-structure  
> based in a (IMO) clear case of recursion — the expos “tries” to get  
> to the secondary key three times, and gets bogged down the first  
> two times in a stubborn D minor, reflecting the rhythm’s inability  
> to break free until it’s third measure.  (It was Ed Hantz who  
> pointed out the “Satz” connection to me when I arrived in Rochester.)
> If you are versed in Knets and Gretchen Foley’s writings, you will  
> find that recursive sum / difference combinations are the essence  
> of George Perle’s music — even Michael Buchler would be satisfied  
> with the rationale for recursion in this setting, I would wager.
> Dave Headlam
> On 3/21/09 6:40 PM, "Thomas Noll" <noll at cs.tu-berlin.de> wrote:
>> Dear Colleagues,
>> last summer I participated in a cross-disciplinary workshop on  
>> "Recursion in Logics, Language and Art" in Berlin, organized by  
>> the logician Ingolf Max.
>> One participant was the well-recognized linguist Manfred  
>> Bierwisch, who argued in favor of a particular difference between  
>> natural language and music in the light of the concept of recursion.
>> He said that music exhibits repetition in a variety of ways, but –  
>> unlike language – it lacks instances of true recursion. My feeling  
>> is that Bierwisch has a point. But I nevertheless feel the  
>> obligation to challenge this assertion.
>> My own contribution to this workshop addressed a transformational  
>> approach to the theory of well-formed modes, and thereby implied a  
>> potential counter-argument on a mathematical level. But I started  
>> to think of other possible counter-arguments to Bierwisch's denial  
>> of recursion in music. 20th century fractal composition techniques  
>> come to mind, but they are still music-theoretical wall-flowers  
>> and wouldn't easily overthrow Bierwisch's position with respect to  
>> common practice repertoire. Event hierarchies in the sense of  
>> Lerdahl and Jackdoff's GTTM are candidates for recursive  
>> structures, but their music-theoretical meaning cannot compete  
>> with the grammatical meaning of derivation trees in linguistics.  
>> In the workshop I spontaneously summarized William Caplin's  
>> analysis (Classical Form, p. 149) of the core of the development  
>> of the 1st movement of Beethoven's F-minor sonata (Op. 2, No.1).  
>> Recall that Caplin interprets formal syntagmatic units with formal  
>> functions, such as presentation, continuation, cadence (closing  
>> function). If we understand the core in terms of a loosely  
>> organized "super-sentence", we find units with the functions  
>> presentation and continuation in recursive embedding - even if  
>> only with depth 2. In particular the presentation of the model  
>> involves a large portion of the secondary theme (including its  
>> presentation phrase and the first bars of its continuation phrase).
>> I would be glad to share this discussion with the list and to  
>> later forward the thread to the participants of the workshop.
>> Sincerely
>> Thomas Noll
>> *********************************************************
>> Thomas Noll
>> http://flp.cs.tu-berlin.de/~noll
>> noll at cs.tu-berlin.de
>> Escola Superior de Musica de Catalunya, Barcelona
>> Departament de Teoria i Composició
>> Tel (priv.):   +34 93 268 75 19
>> Tel (mobil): +34 66 368 12 02
>> *********************************************************
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> -----------------------
> Dave Headlam
> Professor of Music Theory
> Eastman School of Music
> 26 Gibbs St
> Rochester, NY 14604
> (585) 274-1568 office
> dheadlam at esm.rochester.edu
> http://theory.esm.rochester.edu/dave_headlam
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